3.4. Multiple-input gates

Inverters and buffers exhaust the possibilities for single-input gate
circuits. What more can be done with a single logic signal but to buffer it or
invert it? To explore more logic gate possibilities, we must add more input
terminals to the circuit(s).

Adding more input terminals to a logic gate increases the number of input
state possibilities. With a single-input gate such as the inverter or buffer,
there can only be two possible input states: either the input is "high" (1) or
it is "low" (0). As was mentioned previously in this chapter, a two input gate
has four possibilities (00, 01, 10, and 11). A three-input gate has
eight possibilities (000, 001, 010, 011, 100, 101, 110, and 111) for
input states. The number of possible input states is equal to two to the power
of the number of inputs:

This increase in the number of possible input states obviously allows for
more complex gate behavior. Now, instead of merely inverting or amplifying
(buffering) a single "high" or "low" logic level, the output of the gate will be
determined by whatever combination of 1's and 0's is present at the input
terminals.

Since so many combinations are possible with just a few input terminals,
there are many different types of multiple-input gates, unlike single-input
gates which can only be inverters or buffers. Each basic gate type will be
presented in this section, showing its standard symbol, truth table, and
practical operation. The actual TTL circuitry of these different gates will be
explored in subsequent sections.

The AND gate

One of the easiest multiple-input gates to understand is the AND gate,
so-called because the output of this gate will be "high" (1) if and only if
all inputs (first input and the second input and . . .) are
"high" (1). If any input(s) are "low" (0), the output is guaranteed to be in a
"low" state as well.

In case you might have been wondering, AND gates are made with more than
three inputs, but this is less common than the simple two-input variety.

A two-input AND gate's truth table looks like this:

What this truth table means in practical terms is shown in the following
sequence of illustrations, with the 2-input AND gate subjected to all
possibilities of input logic levels. An LED (Light-Emitting Diode) provides
visual indication of the output logic level:

It is only with all inputs raised to "high" logic levels that the AND gate's
output goes "high," thus energizing the LED for only one out of the four input
combination states.

The NAND gate

A variation on the idea of the AND gate is called the NAND gate. The word
"NAND" is a verbal contraction of the words NOT and AND. Essentially, a NAND
gate behaves the same as an AND gate with a NOT (inverter) gate connected to the
output terminal. To symbolize this output signal inversion, the NAND gate symbol
has a bubble on the output line. The truth table for a NAND gate is as one might
expect, exactly opposite as that of an AND gate:

As with AND gates, NAND gates are made with more than two inputs. In such
cases, the same general principle applies: the output will be "low" (0) if and
only if all inputs are "high" (1). If any input is "low" (0), the output will go
"high" (1).

The OR gate

Our next gate to investigate is the OR gate, so-called because the output of
this gate will be "high" (1) if any of the inputs (first input or
the second input or . . .) are "high" (1). The output of an OR gate goes
"low" (0) if and only if all inputs are "low" (0).

A two-input OR gate's truth table looks like this:

The following sequence of illustrations demonstrates the OR gate's function,
with the 2-inputs experiencing all possible logic levels. An LED (Light-Emitting
Diode) provides visual indication of the gate's output logic level:

A condition of any input being raised to a "high" logic level makes the OR
gate's output go "high," thus energizing the LED for three out of the four input
combination states.

The NOR gate

As you might have suspected, the NOR gate is an OR gate with its output
inverted, just like a NAND gate is an AND gate with an inverted output.

NOR gates, like all the other multiple-input gates seen thus far, can be
manufactured with more than two inputs. Still, the same logical principle
applies: the output goes "low" (0) if any of the inputs are made "high" (1). The
output is "high" (1) only when all inputs are "low" (0).

The Negative-AND gate

A Negative-AND gate functions the same as an AND gate with all its inputs
inverted (connected through NOT gates). In keeping with standard gate symbol
convention, these inverted inputs are signified by bubbles. Contrary to most
peoples' first instinct, the logical behavior of a Negative-AND gate is
not the same as a NAND gate. Its truth table, actually, is identical to a
NOR gate:

The Negative-OR gate

Following the same pattern, a Negative-OR gate functions the same as an OR
gate with all its inputs inverted. In keeping with standard gate symbol
convention, these inverted inputs are signified by bubbles. The behavior and
truth table of a Negative-OR gate is the same as for a NAND gate:

The Exclusive-OR gate

The last six gate types are all fairly direct variations on three basic
functions: AND, OR, and NOT. The Exclusive-OR gate, however, is something quite
different.

Exclusive-OR gates output a "high" (1) logic level if the inputs are at
different logic levels, either 0 and 1 or 1 and 0. Conversely, they
output a "low" (0) logic level if the inputs are at the same logic
levels. The Exclusive-OR (sometimes called XOR) gate has both a symbol and a
truth table pattern that is unique:

There are equivalent circuits for an Exclusive-OR gate made up of AND, OR,
and NOT gates, just as there were for NAND, NOR, and the negative-input gates. A
rather direct approach to simulating an Exclusive-OR gate is to start with a
regular OR gate, then add additional gates to inhibit the output from going
"high" (1) when both inputs are "high" (1):

In this circuit, the final AND gate acts as a buffer for the output of the OR
gate whenever the NAND gate's output is high, which it is for the first three
input state combinations (00, 01, and 10). However, when both inputs are "high"
(1), the NAND gate outputs a "low" (0) logic level, which forces the final AND
gate to produce a "low" (0) output.

Another equivalent circuit for the Exclusive-OR gate uses a strategy of two
AND gates with inverters, set up to generate "high" (1) outputs for input
conditions 01 and 10. A final OR gate then allows either of the AND gates'
"high" outputs to create a final "high" output:

Exclusive-OR gates are very useful for circuits where two or more binary
numbers are to be compared bit-for-bit, and also for error detection (parity
check) and code conversion (binary to Grey and vice versa).

The Exclusive-NOR gate

Finally, our last gate for analysis is the Exclusive-NOR gate, otherwise
known as the XNOR gate. It is equivalent to an Exclusive-OR gate with an
inverted output. The truth table for this gate is exactly opposite as for the
Exclusive-OR gate:

As indicated by the truth table, the purpose of an Exclusive-NOR gate is to
output a "high" (1) logic level whenever both inputs are at the same logic
levels (either 00 or 11).

REVIEW:

Rule for an AND gate: output is "high" only if first input and
second input are both "high."

Rule for an OR gate: output is "high" if input A or input B are
"high."

Rule for a NAND gate: output is not "high" if both the first input
and the second input are "high."

Rule for a NOR gate: output is not "high" if either the first input
or the second input are "high."

A Negative-AND gate behaves like a NOR gate.

A Negative-OR gate behaves like a NAND gate.

Rule for an Exclusive-OR gate: output is "high" if the input logic levels
are different.

Rule for an Exclusive-NOR gate: output is "high" if the input logic levels
are the same.